The weak symmetry breaking task with unique input \((n-1)\) -simplex
\(\sigma = \lbrace 0, \hdots , n-1\rbrace \) 
requires that the binary output coloring on the boundary of
\(\chi ^\ell (\sigma )\) 
has the next symmetry property
(assuming the protocol terminates in \(\ell \)  rounds)
on the vertices \(V(\chi ^{\ell }(\sigma ))\) , e.g. [1]}, [2]}, [3]}:
